,xx NAPLEX Blueprint
• 1.3.4 Identify, prevent, and address methods to remedy • 2.3.3 Identify the mechanism of and evidence for the in-
medication nonadherence, misuse, or abuse. compatibility or degradation of a product or preparation
• 1.3.5 Evaluate current drug regimens and recommend and methods for achieving its stability.
pharmacotherapeutic alternatives or modifications.
Area 3 Assess, Recommend, and Provide
Area 2 Assess Safe and Accurate Health Care Information that Promotes
Preparation and Dispensing of Public Health (Approximately 11% of Test)
Medications (Approximately 33% of Test) • 3.1.0 Identify, evaluate, and apply information to pro-
mote optimal health care.
• 2.1.0 Demonstrate the ability to perform calcula-
• 3.1.1 Identify the typical content of specific sources of
tions required to compound, dispense, and administer
drug and health information for both health care pro-
medication.
viders and consumers, and recommend appropriate re-
• 2.1.1 Calculate the quantity of medication to be com-
sources to address questions or needs.
pounded or dispensed; reduce and enlarge formulation
• 3.1.2 Evaluate the suitability, accuracy, and reliability of
quantities and calculate the quantity or ingredients needed
clinical and pharmacoeconomic data by analyzing exper-
to compound the proper amount of the preparation.
imental design, statistical tests, interpreting results, and
• 2.1.2 Calculate nutritional needs and the caloric content
formulating conclusions.
of nutrient sources.
• 3.2.0 Recommend and provide information to educate
• 2.1.3 Calculate the rate of drug administration.
the public and health care professionals regarding medi-
• 2.1.4 Calculate or convert drug concentrations, ratio
cal conditions, wellness, dietary supplements, and medi-
strengths, and/or extent of ionization.
cal devices.
• 2.2.0 Demonstrate the ability to select and dispense
• 3.2.1 Recommend and provide health care information
medications in a manner that promotes safe and effec-
regarding the prevention and treatment of diseases and
tive use.
medical conditions, including emergency patient care
• 2.2.1 Identify drug products by their generic, brand, and/
and vaccinations.
or common names.
• 3.2.2 Recommend and provide health care information
• 2.2.2 Identify whether a particular drug dosage strength
regarding nutrition, lifestyle, and other nondrug mea-
or dosage form is commercially available and whether it
sures that promote health or prevent the progression of a
is available on a nonprescription basis.
disease or medical condition.
• 2.2.3 Identify commercially available drug products by
• 3.2.3 Recommend and provide information regarding
their characteristic physical attributes.
the documented uses, adverse effects, and toxicities of
• 2.2.4 Assess pharmacokinetic parameters and quality
dietary supplements.
assurance data to determine equivalence among manu-
• 3.2.4 Recommend and provide information regarding
factured drug products, and identify products for which
the selection, use, and care of medical/surgical applianc-
documented evidence of inequivalence exists.
es and devices, self-care products, and durable medical
• 2.2.5 Identify and provide information regarding appro-
equipment, as well as products and techniques for self-
priate packaging, storage, handling, administration, and
monitoring of health status and medical conditions.
disposal of medications.
• 2.2.6 Identify and provide information regarding the ap- NABP offers candidates who are preparing for the
propriate use of equipment and apparatus required to NAPLEX—the Pre-NAPLEX, which is similar to the ac-
administer medications. tual NAPLEX and allows candidates to gain experience
• 2.3.0 Demonstrate the knowledge to prepare and com- in answering questions before examination day. The Pre-
pound extemporaneous preparations and sterile products. NAPLEX can be accessed via the Internet at the following
• 2.3.1 Identify techniques, procedures, and equipment website: http://www.nabp.net/prenaplex/. For foreign phar-
related to drug preparation, compounding, and quality macy graduates, the FPGEE Study Guide is available from
assurance. NABP and includes information about the blueprint of the
• 2.3.2 Identify the important physicochemical properties FPGEE, sample questions, and a list of textbooks commonly
of a preparation’s active and inactive ingredients. used in United States pharmacy schools.
drj
,Pharmaceutical
Calculations
1
ROBERT B. GREENWOOD
I. FUNDAMENTALS OF MEASUREMENT AND CALCULATION. The
pharmacist is often required to perform or evaluate a variety of calculations. Many of these calculations
involve the use of direct or inverse proportions. Dimensional (or unit) analysis and approximation can
be useful in solving these problems. In dimensional analysis, dimensions (or units) are included with each
number used in the calculation. Units common to the numerator and denominator may be canceled and
the remaining units provide the units for the final answer. In approximation, each number used in the
calculation is rounded to a single significant digit. Factors common to the numerator and denominator
may be canceled, and the answer to this approximation should be reasonably close to the final exact answer.
A. Ratio and proportion
1. Ratio. The relative magnitude of two like quantities is a ratio, which is expressed as a fraction.
Certain basic principles apply to the ratio, as they do to all fractions.
a. When the two terms of a ratio are multiplied or divided by the same number, the value of the
ratio is unchanged.
_ 2_
1_ 2_
1
3 2 6 3
b. Two ratios with the same value are equivalent. Equivalent ratios have equal cross products and
equal reciprocals. For example:
1_
_ 2
3 6
and
16326
If two ratios are equal, then their reciprocals are equal:
1_
if _ 3_
2 , then _ 6
3 6 1 2
2. Proportion. The expression of the equality of two ratios is a proportion. The product of the
extremes is equal to the product of the means for any proportion. The way to express this, from
the example cited, would be 1:3 2:6, where the means are 3 and 2, and the extremes are 1 and 6.
Furthermore, the numerator of the one fraction equals the product of its denominator and the
other fraction (i.e., one missing term can always be found given the other three terms). Most
pharmaceutical calculations can be performed by use of proportion.
a. Proper ratios. Some pharmacists use proper ratios (in which similar units are used in the numer-
ator and denominator of each ratio) in their proportion calculations. Several examples follow:
(1) If 240 mL of a cough syrup contains 480 mg of dextromethorphan hydrobromide, then
what mass of drug is contained in a child’s dose, 1 teaspoon (5 mL) of syrup?
240 mL _ 480 mg
_
5 mL x mg
480
x _ 10 mg5
240
1
drj
, 2 Chapter 1 I. A
(2) If a child’s dose (5 mL) of a cough syrup contains 10 mg of dextromethorphan hydrobro-
mide, what mass of drug is contained in 240 mL?
240 mL _x mg
_
5 mL 10 mg
240 10 480 mg
x_
5
(3) If the amount of dextromethorphan hydrobromide in 240 mL of cough syrup is 480 mg,
what would be the volume required for a child’s dose of 10 mg?
x mL 10 mg
_ _
240 mL 480 mg
10 240 5mL
x_
480
(4) How many milligrams of dextromethorphan base (molecular weight 271.4) are equiva-
lent to 10 mg of dextromethorphan hydrobromide (molecular weight 352.3)?
x mg 271.4
_ _
10 mg 352.3
271.4 7.7 mg
x 10 _
352.3
b. Mixed ratios. Some pharmacists use mixed ratios (in which dissimilar units are used in the numer-
ator and denominator of each ratio) in their proportion calculations. Such computations generally
give correct answers, providing the conditions in which mixed ratios cannot be used are known. A
later example shows mixed ratios leading to failure in the case of dilution, when inverse proportions
are required. For inverse proportions, similar units must be used in the numerator and denomina-
tor of each ratio. Following is an example of a mixed ratio calculation using the previous problem.
480 mg _240 mg
_
10 mL x mL
x 240 _10 5 mL
480
The same answer is obtained in this example whether we use proper ratios, with similar units
in numerator and denominator, or mixed ratios. This is not the case when dealing with inverse
proportions.
3. Inverse proportion. The most common example of the need for inverse proportion for the pharmacist
is the case of dilution. Whereas in the previous examples of proportion the relationships involved direct
proportion, the case of dilution calls for an inverse proportion (i.e., as volume increases, concentration
decreases). The necessity of using inverse proportions for dilution problems is shown in this example.
If 120 mL of a 10% stock solution is diluted to 240 mL, what is the final concentration? Using
inverse proportion,
x%
120 mL _
_
240 mL 10%
120 _10 5%
240
As expected, the final concentration is one-half of the original concentration because the volume
is doubled. However, if the pharmacist attempts to use direct proportion and neglects to estimate
an appropriate answer, the resulting calculation would provide an answer of 20%, which is twice
the actual concentration.
10%
120 mL _
_
240 mL x%
240 _10 20% (incorrect answer)
120
drj
• 1.3.4 Identify, prevent, and address methods to remedy • 2.3.3 Identify the mechanism of and evidence for the in-
medication nonadherence, misuse, or abuse. compatibility or degradation of a product or preparation
• 1.3.5 Evaluate current drug regimens and recommend and methods for achieving its stability.
pharmacotherapeutic alternatives or modifications.
Area 3 Assess, Recommend, and Provide
Area 2 Assess Safe and Accurate Health Care Information that Promotes
Preparation and Dispensing of Public Health (Approximately 11% of Test)
Medications (Approximately 33% of Test) • 3.1.0 Identify, evaluate, and apply information to pro-
mote optimal health care.
• 2.1.0 Demonstrate the ability to perform calcula-
• 3.1.1 Identify the typical content of specific sources of
tions required to compound, dispense, and administer
drug and health information for both health care pro-
medication.
viders and consumers, and recommend appropriate re-
• 2.1.1 Calculate the quantity of medication to be com-
sources to address questions or needs.
pounded or dispensed; reduce and enlarge formulation
• 3.1.2 Evaluate the suitability, accuracy, and reliability of
quantities and calculate the quantity or ingredients needed
clinical and pharmacoeconomic data by analyzing exper-
to compound the proper amount of the preparation.
imental design, statistical tests, interpreting results, and
• 2.1.2 Calculate nutritional needs and the caloric content
formulating conclusions.
of nutrient sources.
• 3.2.0 Recommend and provide information to educate
• 2.1.3 Calculate the rate of drug administration.
the public and health care professionals regarding medi-
• 2.1.4 Calculate or convert drug concentrations, ratio
cal conditions, wellness, dietary supplements, and medi-
strengths, and/or extent of ionization.
cal devices.
• 2.2.0 Demonstrate the ability to select and dispense
• 3.2.1 Recommend and provide health care information
medications in a manner that promotes safe and effec-
regarding the prevention and treatment of diseases and
tive use.
medical conditions, including emergency patient care
• 2.2.1 Identify drug products by their generic, brand, and/
and vaccinations.
or common names.
• 3.2.2 Recommend and provide health care information
• 2.2.2 Identify whether a particular drug dosage strength
regarding nutrition, lifestyle, and other nondrug mea-
or dosage form is commercially available and whether it
sures that promote health or prevent the progression of a
is available on a nonprescription basis.
disease or medical condition.
• 2.2.3 Identify commercially available drug products by
• 3.2.3 Recommend and provide information regarding
their characteristic physical attributes.
the documented uses, adverse effects, and toxicities of
• 2.2.4 Assess pharmacokinetic parameters and quality
dietary supplements.
assurance data to determine equivalence among manu-
• 3.2.4 Recommend and provide information regarding
factured drug products, and identify products for which
the selection, use, and care of medical/surgical applianc-
documented evidence of inequivalence exists.
es and devices, self-care products, and durable medical
• 2.2.5 Identify and provide information regarding appro-
equipment, as well as products and techniques for self-
priate packaging, storage, handling, administration, and
monitoring of health status and medical conditions.
disposal of medications.
• 2.2.6 Identify and provide information regarding the ap- NABP offers candidates who are preparing for the
propriate use of equipment and apparatus required to NAPLEX—the Pre-NAPLEX, which is similar to the ac-
administer medications. tual NAPLEX and allows candidates to gain experience
• 2.3.0 Demonstrate the knowledge to prepare and com- in answering questions before examination day. The Pre-
pound extemporaneous preparations and sterile products. NAPLEX can be accessed via the Internet at the following
• 2.3.1 Identify techniques, procedures, and equipment website: http://www.nabp.net/prenaplex/. For foreign phar-
related to drug preparation, compounding, and quality macy graduates, the FPGEE Study Guide is available from
assurance. NABP and includes information about the blueprint of the
• 2.3.2 Identify the important physicochemical properties FPGEE, sample questions, and a list of textbooks commonly
of a preparation’s active and inactive ingredients. used in United States pharmacy schools.
drj
,Pharmaceutical
Calculations
1
ROBERT B. GREENWOOD
I. FUNDAMENTALS OF MEASUREMENT AND CALCULATION. The
pharmacist is often required to perform or evaluate a variety of calculations. Many of these calculations
involve the use of direct or inverse proportions. Dimensional (or unit) analysis and approximation can
be useful in solving these problems. In dimensional analysis, dimensions (or units) are included with each
number used in the calculation. Units common to the numerator and denominator may be canceled and
the remaining units provide the units for the final answer. In approximation, each number used in the
calculation is rounded to a single significant digit. Factors common to the numerator and denominator
may be canceled, and the answer to this approximation should be reasonably close to the final exact answer.
A. Ratio and proportion
1. Ratio. The relative magnitude of two like quantities is a ratio, which is expressed as a fraction.
Certain basic principles apply to the ratio, as they do to all fractions.
a. When the two terms of a ratio are multiplied or divided by the same number, the value of the
ratio is unchanged.
_ 2_
1_ 2_
1
3 2 6 3
b. Two ratios with the same value are equivalent. Equivalent ratios have equal cross products and
equal reciprocals. For example:
1_
_ 2
3 6
and
16326
If two ratios are equal, then their reciprocals are equal:
1_
if _ 3_
2 , then _ 6
3 6 1 2
2. Proportion. The expression of the equality of two ratios is a proportion. The product of the
extremes is equal to the product of the means for any proportion. The way to express this, from
the example cited, would be 1:3 2:6, where the means are 3 and 2, and the extremes are 1 and 6.
Furthermore, the numerator of the one fraction equals the product of its denominator and the
other fraction (i.e., one missing term can always be found given the other three terms). Most
pharmaceutical calculations can be performed by use of proportion.
a. Proper ratios. Some pharmacists use proper ratios (in which similar units are used in the numer-
ator and denominator of each ratio) in their proportion calculations. Several examples follow:
(1) If 240 mL of a cough syrup contains 480 mg of dextromethorphan hydrobromide, then
what mass of drug is contained in a child’s dose, 1 teaspoon (5 mL) of syrup?
240 mL _ 480 mg
_
5 mL x mg
480
x _ 10 mg5
240
1
drj
, 2 Chapter 1 I. A
(2) If a child’s dose (5 mL) of a cough syrup contains 10 mg of dextromethorphan hydrobro-
mide, what mass of drug is contained in 240 mL?
240 mL _x mg
_
5 mL 10 mg
240 10 480 mg
x_
5
(3) If the amount of dextromethorphan hydrobromide in 240 mL of cough syrup is 480 mg,
what would be the volume required for a child’s dose of 10 mg?
x mL 10 mg
_ _
240 mL 480 mg
10 240 5mL
x_
480
(4) How many milligrams of dextromethorphan base (molecular weight 271.4) are equiva-
lent to 10 mg of dextromethorphan hydrobromide (molecular weight 352.3)?
x mg 271.4
_ _
10 mg 352.3
271.4 7.7 mg
x 10 _
352.3
b. Mixed ratios. Some pharmacists use mixed ratios (in which dissimilar units are used in the numer-
ator and denominator of each ratio) in their proportion calculations. Such computations generally
give correct answers, providing the conditions in which mixed ratios cannot be used are known. A
later example shows mixed ratios leading to failure in the case of dilution, when inverse proportions
are required. For inverse proportions, similar units must be used in the numerator and denomina-
tor of each ratio. Following is an example of a mixed ratio calculation using the previous problem.
480 mg _240 mg
_
10 mL x mL
x 240 _10 5 mL
480
The same answer is obtained in this example whether we use proper ratios, with similar units
in numerator and denominator, or mixed ratios. This is not the case when dealing with inverse
proportions.
3. Inverse proportion. The most common example of the need for inverse proportion for the pharmacist
is the case of dilution. Whereas in the previous examples of proportion the relationships involved direct
proportion, the case of dilution calls for an inverse proportion (i.e., as volume increases, concentration
decreases). The necessity of using inverse proportions for dilution problems is shown in this example.
If 120 mL of a 10% stock solution is diluted to 240 mL, what is the final concentration? Using
inverse proportion,
x%
120 mL _
_
240 mL 10%
120 _10 5%
240
As expected, the final concentration is one-half of the original concentration because the volume
is doubled. However, if the pharmacist attempts to use direct proportion and neglects to estimate
an appropriate answer, the resulting calculation would provide an answer of 20%, which is twice
the actual concentration.
10%
120 mL _
_
240 mL x%
240 _10 20% (incorrect answer)
120
drj
